Barry allen loves fruit! at the farmers market he bought 88 pieces of fruit. he got twice as many apples as bananas, 5/6 as many kiwis as apples and bananas combined; four more peaches than the sum of bananas and kiwis; half as many grapefruit as apples; and the number of mangos was 20% of the kiwis. how many of each kind of fruit did barry buy? jn

Barry had the following:

8 bananas

12 apples

20 kiwi

32 peaches

8 grapefruit

4 mangos

88 total

Step-by-step explanation:

Each of the amounts of fruit can be written in terms of one variable.  Starting with bananas as 'x', we can then make different values of 'x' to produce all the other numbers of fruits:

bananas = x

apples = 2x (twice as many bananas)

kiwi = 2.5x (5/6 of applies and bananas combined = 5/6(3x) or 2.5x)

peaches = 3.5x + 4 (sum of bananas and kiwis plus four = x + 2.5x + 4)

grapefruit = x (half as many apples = 2x/2)

mango = 0.5x (20% of kiwi = (0.2)(2.5)x)

88 = x + 2x + 2.5x + 3.5x + 4 + x + 0.5x

88 = 10.5x

8 = x (bananas)

apples = 2x or 16; kiwi = 2.5x or 20, peaches = 3.5x + 4 = 32, grapefruit = x or 8, mangos = 0.5x or 4

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for

answer: translate the circles so they share a common center point and dilate circle y by a scale factor of 3.